Interdisciplinary Applied Mathematics

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a few microns.


The amplitude of the deviation from the isothermal condition is a function of the Knudsen and the Mach number. The deviation increases as the Knudsen or the Mach number increases.


At a fixed Knudsen number, changing the Mach number does not lead to any qualitative change in the temperature profile.


At a fixed Mach number the influence of the increase of the Knudsen number is to increase the depth of temperature minimum.


At a fixed Mach number, as the Knudsen number is increased, the (two symmetric) maxima in the temperature profile move near to the wall.

5.5 Heat Transfer in Couette Microflows


In this section a two-dimensional channel extending from y = 0 to y = h is considered. The flow is driven by moving the top wall of the channel with a specified velocity U0. Thus, this case can be a prototype for a microrotor. Assuming a two-dimensional fully developed flow, the Navier-Stokes equations can be simplified to give linear velocity distribution in the channel. This can be written in nondimensional form



Jt = TT( П _ y/h + ^ Kn I 3 (7 — 1) Kn2 Re d% Uq ^    1 + 2-^£lL Kn 27Г    7 Ec dx


The corresponding volumetric flowrate per channel width is


(5.14)

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